Got married 3 years ago here in BsAs. I was here as a visitor, my wife's Argentine. They never even bothered checking the passport for stamps or asked about the legal status. None of that mattered at the time. Its strange that Mari Yagami had to go through making sure her fiance was not "irregular". But that should tell you that nothing here is set in stone, it all depends on what side of the bed the secretary at Registro Civil woke up.
We had to notify Registro Civil of our intent to marry 28 days before the day we wanted to get married. We got our medical done 10 (or was it 7?) days before the day. Went in on the day, got a judge who was in a pretty good mood. He made a couple of jokes, declared us married and the rest is history.
If you want to live here for the next couple of years then I'd suggest get married here since folks here have a thing for paperwork where they refuse to accept legitimate paperwork from other countries for no reason.
To avoid that, get your paperwork done here. The US is a lot more flexible in accepting foreign documents than Argentina.